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40th Annual Symposium on Foundations of Computer Science
Cuts, Trees and Embeddings of Graphs
New York, New York
October 17October 18
ISBN: 0769504094
ASCII Text  x  
Anupam Gupta, Alistair Sinclair, Ilan Newman, Yuri Rabinovich, "Cuts, Trees and Embeddings of Graphs," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 399, 40th Annual Symposium on Foundations of Computer Science, 1999.  
BibTex  x  
@article{ 10.1109/SFFCS.1999.814611, author = {Anupam Gupta and Alistair Sinclair and Ilan Newman and Yuri Rabinovich}, title = {Cuts, Trees and Embeddings of Graphs}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {1999}, issn = {02725428}, pages = {399}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFFCS.1999.814611}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Cuts, Trees and Embeddings of Graphs SN  02725428 SP EP A1  Anupam Gupta, A1  Alistair Sinclair, A1  Ilan Newman, A1  Yuri Rabinovich, PY  1999 KW  Multicommodity flow KW  Sparsest cut KW  <IMG height=18 alt="" src="EQN76.GIF" width=13 border=0> embeddings KW  Finite metric spaces VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
Motivated by many recent algorithmic applications, this paper aims to promote a systematic study of the relationship between the topology of a graph and the metric distortion incurred when the graph is embedded into \math space. The main results are: 1. Explicit constantdistortion embeddings of all seriesparallel graphs, and all graphs with bounded Euler number. These are thus the first natural families known to have constant distortion (strictly greater than 1). Using the above embeddings, we obtain algorithms to approximate the sparsest cut in such graphs to within a constant factor. 2. A constantdistortion embedding of outerplanar graphs into the restricted class of \mathmetrics known as "dominating tree metrics". We also show a lower bound of \math on the distortion for embeddings of seriesparallel graphs into (distributions over) dominating tree metrics. This shows, surprisingly, that such metrics approximate distances very poorly even for families of graphs with low treewidth, and excludes the possibility of using them to explore the finer structure of \mathembeddability.
Index Terms:
Multicommodity flow, Sparsest cut, <IMG height=18 alt="" src="EQN76.GIF" width=13 border=0> embeddings, Finite metric spaces
Citation:
Anupam Gupta, Alistair Sinclair, Ilan Newman, Yuri Rabinovich, "Cuts, Trees and Embeddings of Graphs," focs, pp.399, 40th Annual Symposium on Foundations of Computer Science, 1999
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